Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x + 1$ and $ JT = 6x + 9$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x + 1} = {6x + 9}$ Solve for $x$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({8}) + 1$ $ JT = 6({8}) + 9$ $ CJ = 56 + 1$ $ JT = 48 + 9$ $ CJ = 57$ $ JT = 57$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {57} + {57}$ $ CT = 114$